Systems and methods for estimating values of a continuous wavelet transform

ABSTRACT

According to embodiments, techniques for estimating scalogram energy values in a wedge region of a scalogram are disclosed. A pulse oximetry system including a sensor or probe may be used to receive a photoplethysmograph (PPG) signal from a patient or subject. A scalogram, corresponding to the obtained PPG signal, may be determined. In an arrangement, energy values in the wedge region of the scalogram may be estimated by calculating a set of estimation locations in the wedge region and estimating scalogram energy values at each location. In an arrangement, scalogram energy values may be estimated based on an estimation scheme and by combining scalogram values in a vicinity region. In an arrangement, the vicinity region may include energy values in a resolved region of the scalogram and previously estimated energy values in the wedge region of the scalogram. In an arrangement, one or more signal parameters may be determined based on the resolved and estimated values of the scalogram.

SUMMARY

The present disclosure is related to signal processing systems andmethods, and more particularly, to systems and methods for estimatingscalogram energy values in a wedge region of a scalogram.

In an embodiment, a photoplethysmograph (PPG) signal may be receivedfrom a pulse oximetry system, including from a sensor coupled to thepulse oximetry system. Processing equipment may be used to transform thePPG signal. In an arrangement, the processing equipment may transformthe PPG signal using a continuous wavelet transform, and a scalogram maybe generated from the transformed PPG signal. In an arrangement, one ormore energy values in a wedge region of the scalogram may be estimatedusing an estimated scheme. Further, one or more signal parametersrelated to the PPG signal may be determined or identified based on theestimated energy values. In an arrangement, the determined signalparameters may be output to an output device, including, for example, adisplay or monitor device. In an arrangement, the output device mayinclude an audible alarm.

In an embodiment, the estimation of energy values in the wedge region ofthe scalogram may rely on determining a set of estimation points and aset of locations corresponding to the estimation points in the wedgeregion of the scalogram. In an arrangement, the estimation points may beplaced in a grid-like structure in the wedge region. In an arrangement,a set of estimation parameters may be determined. The set of estimationparameters may include, for example, a statistical estimation technique,a probability of an event, and/or a specification of a size and shape ofa vicinity region. In an arrangement, the vicinity region may enclose apoint to be estimated within the wedge region of the scalogram, and theestimation process may rely on previously estimated values and resolvedscalogram values within the vicinity region to estimate the currentpoint. In an arrangement, the vicinity region may not enclose the pointthat is to be estimated within the wedge region of the scalogram.

In an embodiment, the determined signal parameters may include a patientrespiration rate, a patient oxygen saturation level, a patientrespiration effort level, and/or any suitable combination thereof. In anarrangement, one or more confidence metrics may be determined, where theconfidence metrics relate to the determined signal parameters. Forexample, in an arrangement, each of the confidence metrics may providestatistical or probability-based information on a signal parameter, thatincludes information on the reliability of the signal parameter. In anarrangement, the confidence metrics may be compared to a constraint set,and the estimation scheme may be rerun with different parameters if theconfidence metrics do not jointly satisfy the constraint set. In anarrangement, the determination of the confidence metrics may depend ondetermining energy values and energy structures in a pulse band and/ornoise band of the scalogram.

In an arrangement, the size and shape of the vicinity region may bedetermined based on one or more characteristics of the signal parametersthat are to be determined. For example, the size and shape of thevicinity region may be determined based on expected or previouslyobserved patterns that one or more of the parameters may create in thescalogram.

BRIEF DESCRIPTION OF THE DRAWINGS

The above and other features of the present disclosure, its nature andvarious advantages will be more apparent upon consideration of thefollowing detailed description, taken in conjunction with theaccompanying drawings in which:

FIG. 1 shows an illustrative pulse oximetry system in accordance with anembodiment;

FIG. 2 is a block diagram of the illustrative pulse oximetry system ofFIG. 1 coupled to a patient in accordance with an embodiment;

FIGS. 3( a) and 3(b) show illustrative views of a scalogram derived froma PPG signal in accordance with an embodiment;

FIG. 3( c) shows an illustrative scalogram derived from a signalcontaining two pertinent components in accordance with an embodiment;

FIG. 3( d) shows an illustrative schematic of signals associated with aridge in FIG. 3( c) and illustrative schematics of a further waveletdecomposition of these newly derived signals in accordance with anembodiment;

FIGS. 3( e) and 3(f) are flow charts of illustrative steps involved inperforming an inverse continuous wavelet transform in accordance withembodiments;

FIG. 4 is a block diagram of an illustrative continuous waveletprocessing system in accordance with an embodiment;

FIG. 5 illustrates a PPG signal and corresponding scalogram that may beobtained and/or generated from a pulse oximetry system in accordancewith an embodiment;

FIGS. 6A-B are simplified illustrations of scalograms and techniquesthat may be used to estimate (or otherwise determine) scalogram valuesin a wedge region in accordance with an embodiment;

FIG. 7 depicts an illustrative process for estimating scalogram valuesin a wedge region in accordance with an embodiment;

FIG. 8 depicts an illustrative process for determining a scalogram-basedestimation scheme in accordance with an embodiment;

FIG. 9 depicts an illustrative process for estimating scalogram valuesin a wedge region using a determined estimation scheme, in accordancewith an embodiment; and

FIG. 10 depicts an illustrative process for determining one or moresignal parameters and determining one or more confidence metrics from ascalogram, in accordance with an embodiment.

DETAILED DESCRIPTION

An oximeter is a medical device that may determine the oxygen saturationof the blood. One common type of oximeter is a pulse oximeter, which mayindirectly measure the oxygen saturation of a patient's blood (asopposed to measuring oxygen saturation directly by analyzing a bloodsample taken from the patient) and changes in blood volume in the skin.Ancillary to the blood oxygen saturation measurement, pulse oximetersmay also be used to measure the pulse rate of the patient. Pulseoximeters typically measure and display various blood flowcharacteristics including, but not limited to, the oxygen saturation ofhemoglobin in arterial blood.

An oximeter may include a light sensor that is placed at a site on apatient, typically a fingertip, toe, forehead or earlobe, or in the caseof a neonate, across a foot. The oximeter may pass light using a lightsource through blood perfused tissue and photoelectrically sense theabsorption of light in the tissue. For example, the oximeter may measurethe intensity of light that is received at the light sensor as afunction of time. A signal representing light intensity versus time or amathematical manipulation of this signal (e.g., a scaled versionthereof, a log taken thereof, a scaled version of a log taken thereof,etc.) may be referred to as the photoplethysmograph (PPG) signal. Inaddition, the term “PPG signal,” as used herein, may also refer to anabsorption signal (i.e., representing the amount of light absorbed bythe tissue) or any suitable mathematical manipulation thereof. The lightintensity or the amount of light absorbed may then be used to calculatethe amount of the blood constituent (e.g., oxyhemoglobin) being measuredas well as the pulse rate and when each individual pulse occurs.

The light passed through the tissue is selected to be of one or morewavelengths that are absorbed by the blood in an amount representativeof the amount of the blood constituent present in the blood. The amountof light passed through the tissue varies in accordance with thechanging amount of blood constituent in the tissue and the related lightabsorption. Red and infrared wavelengths may be used because it has beenobserved that highly oxygenated blood will absorb relatively less redlight and more infrared light than blood with a lower oxygen saturation.By comparing the intensities of two wavelengths at different points inthe pulse cycle, it is possible to estimate the blood oxygen saturationof hemoglobin in arterial blood.

When the measured blood parameter is the oxygen saturation ofhemoglobin, a convenient starting point assumes a saturation calculationbased on Lambert-Beer's law. The following notation will be used herein:I(λ,t)=I _(o)(λ)exp(−(sβ _(o)(λ)+(1−s)β_(r)(λ))l(t))  (1)where:

-   λ=wavelength;-   t=time;-   I=intensity of light detected;-   I_(o)=intensity of light transmitted;-   s=oxygen saturation;-   β_(o), β_(r)=empirically derived absorption coefficients; and-   l(t)=a combination of concentration and path length from emitter to    detector as a function of time.

The traditional approach measures light absorption at two wavelengths(e.g., red and infrared (IR)), and then calculates saturation by solvingfor the “ratio of ratios” as follows.

-   1. First, the natural logarithm of (1) is taken (“log” will be used    to represent the natural logarithm) for IR and Red    log I=log I _(o)−(sβ _(o)+(1−s)β_(r))l  (2)-   2. (2) is then differentiated with respect to time

$\begin{matrix}{\frac{{\mathbb{d}\log}\; I}{\mathbb{d}t} = {{- ( {{s\;\beta_{0}} + {( {1 - s} )\beta_{r}}} )}\frac{\mathbb{d}l}{\mathbb{d}t}}} & (3)\end{matrix}$

-   3. Red (3) is divided by IR (3)

$\begin{matrix}{\frac{{\mathbb{d}\log}\;{{I( \lambda_{R} )}/{\mathbb{d}t}}}{{\mathbb{d}\log}\;{{I( \lambda_{IR} )}/{\mathbb{d}t}}} = \frac{{s\;{\beta_{o}( \lambda_{R} )}} + {( {1 - s} ){\beta_{r}( \lambda_{R} )}}}{{s\;{\beta_{o}( \lambda_{IR} )}} + {( {1 - s} ){\beta_{r}( \lambda_{IR} )}}}} & (4)\end{matrix}$

-   4. Solving for s

$s = \frac{{\frac{{\mathbb{d}\log}\;{I( \lambda_{IR} )}}{\mathbb{d}t}{\beta_{r}( \lambda_{R} )}} - {\frac{{\mathbb{d}\log}\;{I( \lambda_{R} )}}{\mathbb{d}t}{\beta_{r}( \lambda_{IR} )}}}{\begin{matrix}{{\frac{{\mathbb{d}\log}\;{I( \lambda_{R} )}}{\mathbb{d}t}( {{\beta_{o}( \lambda_{IR} )} - {\beta_{r}( \lambda_{IR} )}} )} -} \\{\frac{{\mathbb{d}\log}\;{I( \lambda_{IR} )}}{\mathbb{d}t}( {{\beta_{o}( \lambda_{R} )} - {\beta_{r}( \lambda_{R} )}} )}\end{matrix}}$Note in discrete time

$\frac{{\mathbb{d}\log}\;{I( {\lambda,t} )}}{\mathbb{d}t} \simeq {{\log\;{I( {\lambda,t_{2}} )}} - {\log\;{I( {\lambda,t_{1}} )}}}$Using log A−log B=log A/B,

$\frac{{\mathbb{d}\log}\;{I( {\lambda,t} )}}{\mathbb{d}t} \simeq {\log( \frac{I( {t_{2},\lambda} )}{I( {t_{1},\lambda} )} )}$So, (4) can be rewritten as

$\begin{matrix}{{\frac{\frac{{\mathbb{d}\log}\;{I( \lambda_{R} )}}{\mathbb{d}t}}{\frac{{\mathbb{d}\log}\;{I( \lambda_{IR} )}}{\mathbb{d}t}} \simeq \frac{\log( \frac{I( {t_{1},\lambda_{R}} )}{I( {t_{2},\lambda_{R}} )} )}{\log( \frac{I( {t_{1},\lambda_{IR}} )}{I( {t_{2},\lambda_{IR}} )} )}} = R} & (5)\end{matrix}$where R represents the “ratio of ratios.” Solving (4) for s using (5)gives

$s = {\frac{{\beta_{r}( \lambda_{R} )} - {R\;{\beta_{r}( \lambda_{IR} )}}}{{R( {{\beta_{o}( \lambda_{IR} )} - {\beta_{r}( \lambda_{IR} )}} )} - {\beta_{o}( \lambda_{R} )} + {\beta_{T}( \lambda_{R} )}}.}$From (5), R can be calculated using two points (e.g., PPG maximum andminimum), or a family of points. One method using a family of pointsuses a modified version of (5). Using the relationship

$\begin{matrix}{\frac{{\mathbb{d}\log}\; I}{\mathbb{d}t} = \frac{{\mathbb{d}I}/{\mathbb{d}t}}{I}} & (6)\end{matrix}$now (5) becomes

$\begin{matrix}\begin{matrix}{\frac{\frac{{\mathbb{d}\log}\;{I( \lambda_{R} )}}{\mathbb{d}t}}{\frac{{\mathbb{d}\log}\;{I( \lambda_{IR} )}}{\mathbb{d}t}} \simeq \frac{\frac{{I( {t_{2},\lambda_{R}} )} - {I( {t_{1},\lambda_{R}} )}}{I( {t_{1},\lambda_{R}} )}}{\frac{{I( {t_{2},\lambda_{IR}} )} - {I( {t_{1},\lambda_{IR}} )}}{I( {t_{1},\lambda_{IR}} )}}} \\{= \frac{\lbrack {{I( {t_{2},\lambda_{R}} )} - {I( {t_{1},\lambda_{R}} )}} \rbrack{I( {t_{1},\lambda_{IR}} )}}{\lbrack {{I( {t_{2},\lambda_{IR}} )} - {I( {t_{1},\lambda_{IR}} )}} \rbrack{I( {t_{1},\lambda_{R}} )}}} \\{= R}\end{matrix} & (7)\end{matrix}$which defines a cluster of points whose slope of y versus x will give Rwherex(t)=[I(t ₂,λ_(IR))−I(t ₁,λ_(IR))]I(t ₁,λ_(R))y(t)=[I(t ₂,λ_(R))−I(t ₁,λ_(R))]I(t ₁,λ_(IR))y(t)=Rx(t)  (8)

FIG. 1 is a perspective view of an embodiment of a pulse oximetry system10. System 10 may include a sensor 12 and a pulse oximetry monitor 14.Sensor 12 may include an emitter 16 for emitting light at two or morewavelengths into a patient's tissue. A detector 18 may also be providedin sensor 12 for detecting the light originally from emitter 16 thatemanates from the patient's tissue after passing through the tissue.

According to another embodiment and as will be described, system 10 mayinclude a plurality of sensors forming a sensor array in lieu of singlesensor 12. Each of the sensors of the sensor array may be acomplementary metal oxide semiconductor (CMOS) sensor. Alternatively,each sensor of the array may be charged coupled device (CCD) sensor. Inanother embodiment, the sensor array may be made up of a combination ofCMOS and CCD sensors. The CCD sensor may comprise a photoactive regionand a transmission region for receiving and transmitting data whereasthe CMOS sensor may be made up of an integrated circuit having an arrayof pixel sensors. Each pixel may have a photodetector and an activeamplifier.

According to an embodiment, emitter 16 and detector 18 may be onopposite sides of a digit such as a finger or toe, in which case thelight that is emanating from the tissue has passed completely throughthe digit. In an embodiment, emitter 16 and detector 18 may be arrangedso that light from emitter 16 penetrates the tissue and is reflected bythe tissue into detector 18, such as a sensor designed to obtain pulseoximetry data from a patient's forehead.

In an embodiment, the sensor or sensor array may be connected to anddraw its power from monitor 14 as shown. In another embodiment, thesensor may be wirelessly connected to monitor 14 and include its ownbattery or similar power supply (not shown). Monitor 14 may beconfigured to calculate physiological parameters based at least in parton data received from sensor 12 relating to light emission anddetection. In an alternative embodiment, the calculations may beperformed on the monitoring device itself and the result of the oximetryreading may be passed to monitor 14. Further, monitor 14 may include adisplay 20 configured to display the physiological parameters or otherinformation about the system. In the embodiment shown, monitor 14 mayalso include a speaker 22 to provide an audible sound that may be usedin various other embodiments, such as for example, sounding an audiblealarm in the event that a patient's physiological parameters are notwithin a predefined normal range.

In an embodiment, sensor 12, or the sensor array, may be communicativelycoupled to monitor 14 via a cable 24. However, in other embodiments, awireless transmission device (not shown) or the like may be used insteadof or in addition to cable 24.

In the illustrated embodiment, pulse oximetry system 10 may also includea multi-parameter patient monitor 26. The monitor may be cathode raytube type, a flat panel display (as shown) such as a liquid crystaldisplay (LCD) or a plasma display, or any other type of monitor nowknown or later developed. Multi-parameter patient monitor 26 may beconfigured to calculate physiological parameters and to provide adisplay 28 for information from monitor 14 and from other medicalmonitoring devices or systems (not shown). For example, multiparameterpatient monitor 26 may be configured to display an estimate of apatient's blood oxygen saturation generated by pulse oximetry monitor 14(referred to as an “SpO₂” measurement), pulse rate information frommonitor 14 and blood pressure from a blood pressure monitor (not shown)on display 28.

Monitor 14 may be communicatively coupled to multi-parameter patientmonitor 26 via a cable 32 or 34 that is coupled to a sensor input portor a digital communications port, respectively and/or may communicatewirelessly (not shown). In addition, monitor 14 and/or multi-parameterpatient monitor 26 may be coupled to a network to enable the sharing ofinformation with servers or other workstations (not shown). Monitor 14may be powered by a battery (not shown) or by a conventional powersource such as a wall outlet.

FIG. 2 is a block diagram of a pulse oximetry system, such as pulseoximetry system 10 of FIG. 1, which may be coupled to a patient 40 inaccordance with an embodiment. Certain illustrative components of sensor12 and monitor 14 are illustrated in FIG. 2. Sensor 12 may includeemitter 16, detector 18, and encoder 42. In the embodiment shown,emitter 16 may be configured to emit at least two wavelengths of light(e.g., RED and IR) into a patient's tissue 40. Hence, emitter 16 mayinclude a RED light emitting light source such as RED light emittingdiode (LED) 44 and an IR light emitting light source such as IR LED 46for emitting light into the patient's tissue 40 at the wavelengths usedto calculate the patient's physiological parameters. In one embodiment,the RED wavelength may be between about 600 nm and about 700 nm, and theIR wavelength may be between about 800 nm and about 1000 nm. Inembodiments where a sensor array is used in place of single sensor, eachsensor may be configured to emit a single wavelength. For example, afirst sensor emits only a RED light while a second only emits an IRlight.

It will be understood that, as used herein, the term “light” may referto energy produced by radiative sources and may include one or more ofultrasound, radio, microwave, millimeter wave, infrared, visible,ultraviolet, gamma ray or X-ray electromagnetic radiation. As usedherein, light may also include any wavelength within the radio,microwave, infrared, visible, ultraviolet, or X-ray spectra, and thatany suitable wavelength of electromagnetic radiation may be appropriatefor use with the present techniques. Detector 18 may be chosen to bespecifically sensitive to the chosen targeted energy spectrum of theemitter 16.

In an embodiment, detector 18 may be configured to detect the intensityof light at the RED and IR wavelengths. Alternatively, each sensor inthe array may be configured to detect an intensity of a singlewavelength. In operation, light may enter detector 18 after passingthrough the patient's tissue 40. Detector 18 may convert the intensityof the received light into an electrical signal. The light intensity isdirectly related to the absorbance and/or reflectance of light in thetissue 40. That is, when more light at a certain wavelength is absorbedor reflected, less light of that wavelength is received from the tissueby the detector 18. After converting the received light to an electricalsignal, detector 18 may send the signal to monitor 14, wherephysiological parameters may be calculated based on the absorption ofthe RED and IR wavelengths in the patients tissue 40.

In an embodiment, encoder 42 may contain information about sensor 12,such as what type of sensor it is (e.g., whether the sensor is intendedfor placement on a forehead or digit) and the wavelengths of lightemitted by emitter 16. This information may be used by monitor 14 toselect appropriate algorithms, lookup tables and/or calibrationcoefficients stored in monitor 14 for calculating the patient'sphysiological parameters.

Encoder 42 may contain information specific to patient 40, such as, forexample, the patient's age, weight, and diagnosis. This information mayallow monitor 14 to determine, for example, patient-specific thresholdranges in which the patient's physiological parameter measurementsshould fall and to enable or disable additional physiological parameteralgorithms. Encoder 42 may, for instance, be a coded resistor whichstores values corresponding to the type of sensor 12 or the type of eachsensor in the sensor array, the wavelengths of light emitted by emitter16 on each sensor of the sensor array, and/or the patient'scharacteristics. In another embodiment, encoder 42 may include a memoryon which one or more of the following information may be stored forcommunication to monitor 14: the type of the sensor 12; the wavelengthsof light emitted by emitter 16; the particular wavelength each sensor inthe sensor array is monitoring; a signal threshold for each sensor inthe sensor array; any other suitable information; or any combinationthereof.

In an embodiment, signals from detector 18 and encoder 42 may betransmitted to monitor 14. In the embodiment shown, monitor 14 mayinclude a general-purpose microprocessor 48 connected to an internal bus50. Microprocessor 48 may be adapted to execute software, which mayinclude an operating system and one or more applications, as part ofperforming the functions described herein. Also connected to bus 50 maybe a read-only memory (ROM) 52, a random access memory (RAM) 54, userinputs 56, display 20, and speaker 22.

RAM 54 and ROM 52 are illustrated by way of example, and not limitation.Any suitable computer-readable media may be used in the system for datastorage. Computer-readable media are capable of storing information thatcan be interpreted by microprocessor 48. This information may be data ormay take the form of computer-executable instructions, such as softwareapplications, that cause the microprocessor to perform certain functionsand/or computer-implemented methods. Depending on the embodiment, suchcomputer-readable media may include computer storage media andcommunication media. Computer storage media may include volatile andnon-volatile, removable and non-removable media implemented in anymethod or technology for storage of information such ascomputer-readable instructions, data structures, program modules orother data. Computer storage media may include, but is not limited to,RAM, ROM, EPROM, EEPROM, flash memory or other solid state memorytechnology, CD-ROM, DVD, or other optical storage, magnetic cassettes,magnetic tape, magnetic disk storage or other magnetic storage devices,or any other medium which can be used to store the desired informationand which can be accessed by components of the system.

In the embodiment shown, a time processing unit (TPU) 58 may providetiming control signals to a light drive circuitry 60, which may controlwhen emitter 16 is illuminated and multiplexed timing for the RED LED 44and the IR LED 46. TPU 58 may also control the gating-in of signals fromdetector 18 through an amplifier 62 and a switching circuit 64. Thesesignals are sampled at the proper time, depending upon which lightsource is illuminated. The received signal from detector 18 may bepassed through an amplifier 66, a low pass filter 68, and ananalog-to-digital converter 70. The digital data may then be stored in aqueued serial module (QSM) 72 (or buffer) for later downloading to RAM54 as QSM 72 fills up. In one embodiment, there may be multiple separateparallel paths having amplifier 66, filter 68, and A/D converter 70 formultiple light wavelengths or spectra received.

In an embodiment, microprocessor 48 may determine the patient'sphysiological parameters, such as SPO₂ and pulse rate, using variousalgorithms and/or look-up tables based on the value of the receivedsignals and/or data corresponding to the light received by detector 18.Signals corresponding to information about patient 40, and particularlyabout the intensity of light emanating from a patient's tissue overtime, may be transmitted from encoder 42 to a decoder 74. These signalsmay include, for example, encoded information relating to patientcharacteristics. Decoder 74 may translate these signals to enable themicroprocessor to determine the thresholds based on algorithms orlook-up tables stored in ROM 52. User inputs 56 may be used to enterinformation about the patient, such as age, weight, height, diagnosis,medications, treatments, and so forth. In an embodiment, display 20 mayexhibit a list of values which may generally apply to the patient, suchas, for example, age ranges or medication families, which the user mayselect using user inputs 56.

The optical signal through the tissue can be degraded by noise, amongother sources. One source of noise is ambient light that reaches thelight detector. Another source of noise is electromagnetic coupling fromother electronic instruments. Movement of the patient also introducesnoise and affects the signal. For example, the contact between thedetector and the skin, or the emitter and the skin, can be temporarilydisrupted when movement causes either to move away from the skin. Inaddition, because blood is a fluid, it responds differently than thesurrounding tissue to inertial effects, thus resulting in momentarychanges in volume at the point to which the oximeter probe is attached.

Noise (e.g., from patient movement) can degrade a pulse oximetry signalrelied upon by a physician, without the physician's awareness. This isespecially true if the monitoring of the patient is remote, the motionis too small to be observed, or the doctor is watching the instrument orother parts of the patient, and not the sensor site. Processing pulseoximetry (i.e., PPG) signals may involve operations that reduce theamount of noise present in the signals or otherwise identify noisecomponents in order to prevent them from affecting measurements ofphysiological parameters derived from the PPG signals. PPG signals maybe taken herein to mean processed or filtered PPG signals.

It will be understood that the present disclosure is applicable to anysuitable signals and that PPG signals are used merely for illustrativepurposes. Those skilled in the art will recognize that the presentdisclosure has wide applicability to other signals including, but notlimited to other biosignals (e.g., electrocardiogram,electroencephalogram, electrogastrogram, electromyogram, heart ratesignals, pathological sounds, ultrasound, or any other suitablebiosignal), dynamic signals, non-destructive testing signals, conditionmonitoring signals, fluid signals, geophysical signals, astronomicalsignals, electrical signals, financial signals including financialindices, sound and speech signals, chemical signals, meteorologicalsignals including climate signals, and/or any other suitable signal,and/or any combination thereof.

In one embodiment, a PPG signal may be transformed using a continuouswavelet transform. Information derived from the transform of the PPGsignal (i.e., in wavelet space) may be used to provide measurements ofone or more physiological parameters.

The continuous wavelet transform of a signal x(t) in accordance with thepresent disclosure may be defined as

$\begin{matrix}{{T( {a,b} )} = {\frac{1}{\sqrt{a}}{\int_{- \infty}^{+ \infty}{{x(t)}{\psi^{*}( \frac{t - b}{a} )}\ {\mathbb{d}t}}}}} & (9)\end{matrix}$where ψ*(t) is the complex conjugate of the wavelet function ψ(t), a isthe dilation parameter of the wavelet and b is the location parameter ofthe wavelet. The transform given by equation (9) may be used toconstruct a representation of a signal on a transform surface. Thetransform may be regarded as a time-scale representation. Wavelets arecomposed of a range of frequencies, one of which may be denoted as thecharacteristic frequency of the wavelet, where the characteristicfrequency associated with the wavelet is inversely proportional to thescale a. One example of a characteristic frequency is the dominantfrequency. Each scale of a particular wavelet may have a differentcharacteristic frequency. The underlying mathematical detail requiredfor the implementation within a time-scale can be found, for example, inPaul S. Addison, The Illustrated Wavelet Transform Handbook (Taylor &Francis Group 2002), which is hereby incorporated by reference herein inits entirety.

The continuous wavelet transform decomposes a signal using wavelets,which are generally highly localized in time. The continuous wavelettransform may provide a higher resolution relative to discretetransforms, thus providing the ability to garner more information fromsignals than typical frequency transforms such as Fourier transforms (orany other spectral techniques) or discrete wavelet transforms.Continuous wavelet transforms allow for the use of a range of waveletswith scales spanning the scales of interest of a signal such that smallscale signal components correlate well with the smaller scale waveletsand thus manifest at high energies at smaller scales in the transform.Likewise, large scale signal components correlate well with the largerscale wavelets and thus manifest at high energies at larger scales inthe transform. Thus, components at different scales may be separated andextracted in the wavelet transform domain. Moreover, the use of acontinuous range of wavelets in scale and time position allows for ahigher resolution transform than is possible relative to discretetechniques.

In addition, transforms and operations that convert a signal or anyother type of data into a spectral (i.e., frequency) domain necessarilycreate a series of frequency transform values in a two-dimensionalcoordinate system where the two dimensions may be frequency and, forexample, amplitude. For example, any type of Fourier transform wouldgenerate such a two-dimensional spectrum. In contrast, wavelettransforms, such as continuous wavelet transforms, are required to bedefined in a three-dimensional coordinate system and generate a surfacewith dimensions of time, scale and, for example, amplitude. Hence,operations performed in a spectral domain cannot be performed in thewavelet domain; instead the wavelet surface must be transformed into aspectrum (i.e., by performing an inverse wavelet transform to convertthe wavelet surface into the time domain and then performing a spectraltransform from the time domain). Conversely, operations performed in thewavelet domain cannot be performed in the spectral domain; instead aspectrum must first be transformed into a wavelet surface (i.e., byperforming an inverse spectral transform to convert the spectral domaininto the time domain and then performing a wavelet transform from thetime domain). Nor does a cross-section of the three-dimensional waveletsurface along, for example, a particular point in time equate to afrequency spectrum upon which spectral-based techniques may be used. Atleast because wavelet space includes a time dimension, spectraltechniques and wavelet techniques are not interchangeable. It will beunderstood that converting a system that relies on spectral domainprocessing to one that relies on wavelet space processing would requiresignificant and fundamental modifications to the system in order toaccommodate the wavelet space processing (e.g., to derive arepresentative energy value for a signal or part of a signal requiresintegrating twice, across time and scale, in the wavelet domain while,conversely, one integration across frequency is required to derive arepresentative energy value from a spectral domain). As a furtherexample, to reconstruct a temporal signal requires integrating twice,across time and scale, in the wavelet domain while, conversely, oneintegration across frequency is required to derive a temporal signalfrom a spectral domain. It is well known in the art that, in addition toor as an alternative to amplitude, parameters such as energy density,modulus, phase, among others may all be generated using such transformsand that these parameters have distinctly different contexts andmeanings when defined in a two-dimensional frequency coordinate systemrather than a three-dimensional wavelet coordinate system. For example,the phase of a Fourier system is calculated with respect to a singleorigin for all frequencies while the phase for a wavelet system isunfolded into two dimensions with respect to a wavelet's location (oftenin time) and scale.

The energy density function of the wavelet transform, the scalogram, isdefined asS(a,b)=|T(a,b)|²  (10)where ‘∥’ is the modulus operator. The scalogram may be resealed foruseful purposes. One common rescaling is defined as

$\begin{matrix}{{S_{R}( {a,b} )} = \frac{{{T( {a,b} )}}^{2}}{a}} & (11)\end{matrix}$and is useful for defining ridges in wavelet space when, for example,the Morlet wavelet is used. Ridges are defined as the locus of points oflocal maxima in the plane. Any reasonable definition of a ridge may beemployed in the method. Also included as a definition of a ridge hereinare paths displaced from the locus of the local maxima. A ridgeassociated with only the locus of points of local maxima in the planeare labeled a “maxima ridge”.

For implementations requiring fast numerical computation, the wavelettransform may be expressed as an approximation using Fourier transforms.Pursuant to the convolution theorem, because the wavelet transform isthe cross-correlation of the signal with the wavelet function, thewavelet transform may be approximated in terms of an inverse FFT of theproduct of the Fourier transform of the signal and the Fourier transformof the wavelet for each required a scale and then multiplying the resultby √{square root over (a)}.

In the discussion of the technology which follows herein, the“scalogram” may be taken to include all suitable forms of resealingincluding, but not limited to, the original unscaled waveletrepresentation, linear rescaling, any power of the modulus of thewavelet transform, or any other suitable rescaling. In addition, forpurposes of clarity and conciseness, the term “scalogram” shall be takento mean the wavelet transform, T(a,b) itself, or any part thereof. Forexample, the real part of the wavelet transform, the imaginary part ofthe wavelet transform, the phase of the wavelet transform, any othersuitable part of the wavelet transform, or any combination thereof isintended to be conveyed by the term “scalogram”.

A scale, which may be interpreted as a representative temporal period,may be converted to a characteristic frequency of the wavelet function.The characteristic frequency associated with a wavelet of arbitrary ascale is given by

$\begin{matrix}{f = \frac{f_{c}}{a}} & (12)\end{matrix}$where f_(c), the characteristic frequency of the mother wavelet (i.e.,at a=1), becomes a scaling constant and f is the representative orcharacteristic frequency for the wavelet at arbitrary scale a.

Any suitable wavelet function may be used in connection with the presentdisclosure. One of the most commonly used complex wavelets, the Morletwavelet, is defined as:ψ(t)=π^(−1/4)(e ^(i2πf) ⁰ ^(t) −e ^(−(2πf) ⁰ ⁾ ² ^(/2))e ^(−t) ²^(/2)  (13)where f₀ is the central frequency of the mother wavelet. The second termin the parenthesis is known as the correction term, as it corrects forthe non-zero mean of the complex sinusoid within the Gaussian window. Inpractice, it becomes negligible for values of f₀>>0 and can be ignored,in which case, the Morlet wavelet can be written in a simpler form as

$\begin{matrix}{{\psi(t)} = {\frac{1}{\pi^{1/4}}{\mathbb{e}}^{{\mathbb{i}}\; 2\pi\; f_{0}t}{\mathbb{e}}^{{- t^{2}}/2}}} & (14)\end{matrix}$

This wavelet is a complex wave within a scaled Gaussian envelope. Whileboth definitions of the Morlet wavelet are included herein, the functionof equation (14) is not strictly a wavelet as it has a non-zero mean(i.e., the zero frequency term of its corresponding energy spectrum isnon-zero). However, it will be recognized by those skilled in the artthat equation (14) may be used in practice with f₀>>0 with minimal errorand is included (as well as other similar near wavelet functions) in thedefinition of a wavelet herein. A more detailed overview of theunderlying wavelet theory, including the definition of a waveletfunction, can be found in the general literature. Discussed herein ishow wavelet transform features may be extracted from the waveletdecomposition of signals. For example, wavelet decomposition of PPGsignals may be used to provide clinically useful information within amedical device.

Pertinent repeating features in a signal give rise to a time-scale bandin wavelet space or a resealed wavelet space. For example, the pulsecomponent of a PPG signal produces a dominant band in wavelet space ator around the pulse frequency. FIGS. 3( a) and (b) show two views of anillustrative scalogram derived from a PPG signal, according to anembodiment. The figures show an example of the band caused by the pulsecomponent in such a signal. The pulse band is located between the dashedlines in the plot of FIG. 3( a). The band is formed from a series ofdominant coalescing features across the scalogram. This can be clearlyseen as a raised band across the transform surface in FIG. 3( b) locatedwithin the region of scales indicated by the arrow in the plot(corresponding to 60 beats per minute). The maxima of this band withrespect to scale is the ridge. The locus of the ridge is shown as ablack curve on top of the band in FIG. 3( b). By employing a suitableresealing of the scalogram, such as that given in equation (11), theridges found in wavelet space may be related to the instantaneousfrequency of the signal. In this way, the pulse rate may be obtainedfrom the PPG signal. Instead of rescaling the scalogram, a suitablepredefined relationship between the scale obtained from the ridge on thewavelet surface and the actual pulse rate may also be used to determinethe pulse rate.

By mapping the time-scale coordinates of the pulse ridge onto thewavelet phase information gained through the wavelet transform,individual pulses may be captured. In this way, both times betweenindividual pulses and the timing of components within each pulse may bemonitored and used to detect heart beat anomalies, measure arterialsystem compliance, or perform any other suitable calculations ordiagnostics. Alternative definitions of a ridge may be employed.Alternative relationships between the ridge and the pulse frequency ofoccurrence may be employed.

As discussed above, pertinent repeating features in the signal give riseto a time-scale band in wavelet space or a resealed wavelet space. For aperiodic signal, this band remains at a constant scale in the time-scaleplane. For many real signals, especially biological signals, the bandmay be non-stationary; varying in scale, amplitude, or both over time.FIG. 3( c) shows an illustrative schematic of a wavelet transform of asignal containing two pertinent components leading to two bands in thetransform space, according to an embodiment. These bands are labeledband A and band B on the three-dimensional schematic of the waveletsurface. In this embodiment, the band ridge is defined as the locus ofthe peak values of these bands with respect to scale. For purposes ofdiscussion, it may be assumed that band B contains the signalinformation of interest. This will be referred to as the “primary band”.In addition, it may be assumed that the system from which the signaloriginates, and from which the transform is subsequently derived,exhibits some form of coupling between the signal components in band Aand band B. When noise or other erroneous features are present in thesignal with similar spectral characteristics of the features of band Bthen the information within band B can become ambiguous (i.e., obscured,fragmented or missing). In this case, the ridge of band A may befollowed in wavelet space and extracted either as an amplitude signal ora scale signal which will be referred to as the “ridge amplitudeperturbation” (RAP) signal and the “ridge scale perturbation” (RSP)signal, respectively. The RAP and RSP signals may be extracted byprojecting the ridge onto the time-amplitude or time-scale planes,respectively. The top plots of FIG. 3( d) show a schematic of the RAPand RSP signals associated with ridge A in FIG. 3( c). Below these RAPand RSP signals are schematics of a further wavelet decomposition ofthese newly derived signals. This secondary wavelet decomposition allowsfor information in the region of band B in FIG. 3( c) to be madeavailable as band C and band D. The ridges of bands C and D may serve asinstantaneous time-scale characteristic measures of the signalcomponents causing bands C and D. This technique, which will be referredto herein as secondary wavelet feature decoupling (SWFD), may allowinformation concerning the nature of the signal components associatedwith the underlying physical process causing the primary band B (FIG. 3(c)) to be extracted when band B itself is obscured in the presence ofnoise or other erroneous signal features.

In some instances, an inverse continuous wavelet transform may bedesired, such as when modifications to a scalogram (or modifications tothe coefficients of a transformed signal) have been made in order to,for example, remove artifacts. In one embodiment, there is an inversecontinuous wavelet transform which allows the original signal to berecovered from its wavelet transform by integrating over all scales andlocations, a and b:

$\begin{matrix}{{x(t)} = {\frac{1}{C_{g}}{\int_{- \infty}^{\infty}{\int_{0}^{\infty}{{T( {a,b} )}\frac{1}{\sqrt{a}}{\psi( \frac{t - b}{a} )}\frac{\ {{\mathbb{d}a}\ {\mathbb{d}b}}}{a^{2}}}}}}} & (15)\end{matrix}$which may also be written as:

$\begin{matrix}{{x(t)} = {\frac{1}{C_{g}}{\int_{- \infty}^{\infty}{\int_{0}^{\infty}{{T( {a,b} )}{\psi_{a,b}(t)}\ \frac{{\mathbb{d}a}\ {\mathbb{d}b}}{a^{2}}}}}}} & (16)\end{matrix}$where C_(g) is a scalar value known as the admissibility constant. It iswavelet type dependent and may be calculated from:

$\begin{matrix}{C_{g} = {\int_{0}^{\infty}{\frac{{{\hat{\psi}(f)}}^{2}}{f}\ {\mathbb{d}f}}}} & (17)\end{matrix}$FIG. 3( e) is a flow chart of illustrative steps that may be taken toperform an inverse continuous wavelet transform in accordance with theabove discussion. An approximation to the inverse transform may be madeby considering equation (15) to be a series of convolutions acrossscales. It shall be understood that there is no complex conjugate here,unlike for the cross correlations of the forward transform. As well asintegrating over all of a and b for each time t, this equation may alsotake advantage of the convolution theorem which allows the inversewavelet transform to be executed using a series of multiplications. FIG.3( f) is a flow chart of illustrative steps that may be taken to performan approximation of an inverse continuous wavelet transform. It will beunderstood that any other suitable technique for performing an inversecontinuous wavelet transform may be used in accordance with the presentdisclosure.

FIG. 4 is an illustrative continuous wavelet processing system inaccordance with an embodiment. In this embodiment, input signalgenerator 410 generates an input signal 416. As illustrated, inputsignal generator 410 may include oximeter 420 coupled to sensor 418,which may provide as input signal 416, a PPG signal. It will beunderstood that input signal generator 410 may include any suitablesignal source, signal generating data, signal generating equipment, orany combination thereof to produce signal 416. Signal 416 may be anysuitable signal or signals, such as, for example, biosignals (e.g.,electrocardiogram, electroencephalogram, electrogastrogram,electromyogram, heart rate signals, pathological sounds, ultrasound, orany other suitable biosignal), dynamic signals, non-destructive testingsignals, condition monitoring signals, fluid signals, geophysicalsignals, astronomical signals, electrical signals, financial signalsincluding financial indices, sound and speech signals, chemical signals,meteorological signals including climate signals, and/or any othersuitable signal, and/or any combination thereof.

In this embodiment, signal 416 may be coupled to processor 412.Processor 412 may be any suitable software, firmware, and/or hardware,and/or combinations thereof for processing signal 416. For example,processor 412 may include one or more hardware processors (e.g.,integrated circuits), one or more software modules, computer-readablemedia such as memory, firmware, or any combination thereof. Processor412 may, for example, be a computer or may be one or more chips (i.e.,integrated circuits). Processor 412 may perform the calculationsassociated with the continuous wavelet transforms of the presentdisclosure as well as the calculations associated with any suitableinterrogations of the transforms. Processor 412 may perform any suitablesignal processing of signal 416 to filter signal 416, such as anysuitable band-pass filtering, adaptive filtering, closed-loop filtering,and/or any other suitable filtering, and/or any combination thereof.

Processor 412 may be coupled to one or more memory devices (not shown)or incorporate one or more memory devices such as any suitable volatilememory device (e.g., RAM, registers, etc.), non-volatile memory device(e.g., ROM, EPROM, magnetic storage device, optical storage device,flash memory, etc.), or both. The memory may be used by processor 412to, for example, store data corresponding to a continuous wavelettransform of input signal 416, such as data representing a scalogram. Inone embodiment, data representing a scalogram may be stored in RAM ormemory internal to processor 412 as any suitable three-dimensional datastructure such as a three-dimensional array that represents thescalogram as energy levels in a time-scale plane. Any other suitabledata structure may be used to store data representing a scalogram.

Processor 412 may be coupled to output 414. Output 414 may be anysuitable output device such as, for example, one or more medical devices(e.g., a medical monitor that displays various physiological parameters,a medical alarm, or any other suitable medical device that eitherdisplays physiological parameters or uses the output of processor 412 asan input), one or more display devices (e.g., monitor, PDA, mobilephone, any other suitable display device, or any combination thereof),one or more audio devices, one or more memory devices (e.g., hard diskdrive, flash memory, RAM, optical disk, any other suitable memorydevice, or any combination thereof), one or more printing devices, anyother suitable output device, or any combination thereof.

It will be understood that system 400 may be incorporated into system 10(FIGS. 1 and 2) in which, for example, input signal generator 410 may beimplemented as parts of sensor 12 and monitor 14 and processor 412 maybe implemented as part of monitor 14.

FIG. 5 illustrates a PPG signal and corresponding scalogram that mayobtained and/or generated from a pulse oximetry system, such as pulseoximetry system 10 (FIG. 1), in accordance with an embodiment. Plot 500displays time on the horizontal axis (“x-axis”) and amplitude values ofPPG signal 510 on the vertical axis (“y-axis”). PPG signal 510 may beobtained from a patient, such as patient 40 (FIG. 2), using a sensorsuch as sensor 12 (FIG. 1). Alternatively, PPG signal 510 may beobtained by averaging or otherwise combining multiple signals derivedfrom a suitable sensor array, as discussed in relation to FIG. 1. Plot500 may be displayed using any suitable display device such as, forexample, monitor 20 (FIG. 1), display 28 (FIG. 1), a PDA, a mobiledevice, or any other suitable display device. Additionally, plot 500 maybe displayed on multiple display devices.

PPG signal 510 may exhibit an oscillatory behavior versus time, and mayinclude several undulations of varying signal amplitude level andfrequency. The size, shape, and frequency of the undulations of PPGsignal 510 may be indicative of an underlying parameter or phenomenonthat is to be detected or estimated. For example, PPG signal 510 mayreflect the breaths or breathing cycle of a patient, such as patient 40(FIG. 2), and/or may be used determine the respiration rate of thepatient. PPG signal 510 may be a processed version of a preliminary PPGsignal obtained by, for example, sensor 12 (FIG. 1). PPG signal 510 maycontain erroneous or otherwise undesirable artifacts due to, forexample, patient movement, equipment failure, and/or various noisesources, including thermal noise, shot noise, flicker noise, burstnoise, and/or electrical noise caused by light pollution. These andother noise sources may be introduced, for example, through sensor 12(FIG. 1), and/or cables 24, 32, and 34 (all of FIG. 1).

Scalogram 550 may be determined from, and correspond to, PPG signal 510.Scalogram 550 may be derived from PPG signal 510 using a processor suchas processor 412 (FIG. 2) or microprocessor 48 (FIG. 2) of pulseoximetry monitor 14 (FIG. 1) to first compute the continuous wavelettransform of PPG signal 510. In scalogram 550, the horizontal axisdenotes time and the vertical axis denotes scale. The darkness of theshading of a point in scalogram 550, denotes the relative energy valueof the point. Scalogram 550 may include post-processing performed, forexample, using user inputs 56 (FIG. 2), to set predetermined energyvalues if they are above and/or below predetermined thresholds. Thepredetermined energy and threshold values may be stored in ROM 52 (FIG.2) and/or RAM 54 (FIG. 2). Alternatively, the energy and thresholdvalues may not be predetermined, but rather, controlled by an operator,using, for example, user inputs 56 (FIG. 2) and a display such asmonitor 26 (FIG. 1) or display 20 or 28 (both of FIG. 1).

Scalogram 550 may include distinct scale bands (i.e. ranges of scalevalues) including pulse band 560 and noise band 570. Pulse band 560 maycontain an energy structure and energy values that reflect the pulsecomponent of PPG signal 510. Pulse band 560 may be generallycharacterized by moderate to high energy values within the band andareas of lower energy at surrounding scale values. Noise band 570 maycontain an energy structure and energy values that reflect general typesof noise that may be present in PPG signal 510. For example, noise band570 may include the effects of thermal noise, shot noise, flicker noise,burst noise, and/or electrical noise caused by light pollution. Noiseband 570 may be generally characterized as having a less coherent energystructure and/or a lower energy level than pulse band 560.

Scalogram 550 may include wedge region 580. Wedge region 580 appears ina scalogram in the lower-right hand corner, and may represent a regionof unresolved or partially resolved scalogram values. Wedge region 580may form because future values of the underlying PPG signal, forexample, PPG signal 510, are needed to fully resolve actual scalogramvalues. For example, in an embodiment, the infinite future values of thePPG signal may be needed to fully resolve scalogram values in wedgeregion 580, for example, when using the Morlet wavelet. Alternatively,rather than an infinite PPG signal, an operator may determine the degreeof resolution needed to sufficiently “resolve” scalogram 550 for anypractical application, and this information may be stored, for example,in ROM 52 (FIG. 2) or RAM 54 (FIG. 2). For example, an operator maydetermine the length of section of future signal values needed, forexample, from PPG signal 510, so that the error between the true wavelettransform of the signal and the computed wavelet transform of the signalis acceptable for a given application, such as determining a patientrespiration rate, oxygen saturation level, and/or respiration effortlevel. In an embodiment, the Morlet wavelet (or any otherinfinite-length wavelet) is computed using a section of an underlyingsignal that is of finite length, for example, having three standarddeviations from the center of a Gaussian window forming part of thewavelet function, and longer or shorter sections of the underlyingsignal may also be used to resolve values in scalogram 500 in apractical manner. Typically, the length of the required section offuture PPG values depends on the scale value for which the scalogram isbeing resolved, with larger scales (smaller values on the scale axis)requiring larger sections of the underlying signal, for example, PPGsignal 510, to be resolved. Therefore, wedge region 580 may, in practiceclosely resemble a wedge shape, as shown in FIG. 5, but it mayalternatively appear as a more or less regular shape. The energy valuesof scalogram 550 within wedge region 580 (i.e., energy values that haveyet to be resolved to a sufficient degree) may be discontinuous fromthose outside of wedge region 580 and may include spurious and/orerroneous features, including noise, and/or other undesirablecomponents. Therefore, in an embodiment, the displayed scalogram valuesin wedge region 580 may be set to low-energy predetermined values set bya user or operator prior to display, for example, on monitor 26 (FIG. 1)or display 20 or 28 (both of FIG. 1). For example, the scalogram valuesin wedge region 580 have been set to a constant low-energy value(denoted by dark black shading) to avoid obfuscating the fully resolvedvalues of the scalogram present in resolved region 575. As describedabove, wedge region 580 may contain a significant number of erroneousvalues with spurious energy, and this is due to the apparent sharpdiscontinuity at the end of the underlying signal, for example, PPGsignal 510. This is due to the wavelet being computed for the known partof the underlying signal and not for future values of the underlyingsignal, which produces the same scalogram as if the remaining values(i.e., future values) of the underlying signal are set to zero(producing an apparent large discontinuity).

A patient parameter may be determined based on interpolating,extrapolating, and/or extracting characteristics of scalogram 550. Forexample, the oxygen saturation, respiration rate, and/or the respirationeffort level of a patient such as patient 40 (FIG. 2) may be determinedfrom scalogram 550. The characteristics of scalogram 550 mayadditionally or alternatively be use to identity and/or filter noise orinterference in PPG signal 510.

The discontinuous, spurious, erroneous and/or inaccurate energy valuesin wedge region 580 may typically degrade the overall quality ofscalogram 550, and may thus degrade the detection and/or estimation ofparameters, such as physiological parameters of patient 40 (FIG. 2).Alternatively, if scalogram values in wedge region 580 are ignored, thenthe extracted parameter values may be based on old and/or outdatedscalogram data, which may lead to outdated and/or ineffective estimatesof a parameter or parameters to be estimated, such as those of patient40 (FIG. 2). For example, a patient respiration rate may be computedbased on scalogram values occurring prior to time 585 if the wedgeregion of scalogram 550 is ignored. This approach may yield outdatedparameter calculations if the time-rate of change of the patientrespiration rate is sufficiently rapid.

Therefore, it may be desired to use wedge region 580 of the scalogram tocompute parameter estimates or extract relevant parameters, while at thesame time limiting the apparent discontinuities and erroneous energyvalues present in wedge region 580. For example, improved techniques forestimating the true scalogram values at various locations within wedgeregion 580 may be desirable. In an embodiment, an improved estimate ofthe scalogram value at a point, for example, point 587, in wedge region580 may be determined from the scalogram energies in the immediateneighborhood of point 587. In this way, better estimates of thescalogram value at point 587 may be determined from known scalogramvalues outside of wedge region 580, as well as from previously estimatedscalogram values within wedge region 580. Thus, in this manner,estimates of scalogram values in wedge region 580 are found by extendingknown information about a scalogram (i.e., scalogram 550) rather than anunderlying signal (i.e., PPG signal 510). In an embodiment, a techniquefor estimating the scalogram value at point 575 may also rely oninformation from the physiological system producing the underlyingsignal, for example, PPG signal 510 or any other biosignal. For example,estimation of the scalogram value at point 587 may involveparameterization based on known techniques in the art, where parametersmay depend on past and/or current characteristics of patient 40 (FIG.2), room conditions such as temperature and lighting, template matchingwith existing biological models, and/or on any other suitable technique.

Although the techniques disclosed herein are described in terms of PPGsignal 510, the disclosed techniques may be applied to any othersuitable signal. For example, the disclosed techniques may be applied toother biosignals including transthoracic impedance signals, and/orcapnograph signals. Further, PPG signal 510 or any other related signalmay be obtained from a source other than pulse oximeter system 10 (FIG.1). For example, PPG signal 510 may be obtained from another type ofmedical device or from non-medical devices including a general signaloscilloscope, signal generator, and/or waveform analyzer. PPG signal 510may be a simplified embodiment of a PPG signal, or other type of signal,measured in practice. The techniques disclosed herein may be applied tosignals that, for example, have more or less frequent undulations thanPPG signal 510, time-variant mean amplitude values, noise patterns,and/or discontinuities. The techniques described herein may be appliedto PPG signals that do not resemble the time-varying pattern of PPGsignal 510 shown in FIG. 5.

FIG. 6A is a simplified illustration of a scalogram and technique thatmay be used to estimate or otherwise determine scalogram values in awedge region. Scalogram 600 includes resolved region 610 and wedgeregion 620, which may correspond to resolved region 575 (FIG. 5) andwedge region 580 (FIG. 5), respectively, of scalogram 500 (FIG. 5). Animproved technique to determine scalogram values in wedge region 620will now be summarized, and more detailed embodiments and features ofthe technique will be described in relation to FIGS. 7-10. First, anumber and a set of locations within wedge region 620 may be determinedfor which scalogram estimates are to be made. For example the pointsdenoted by ″, in wedge region 620 may denote the location and numberpoints for which scalogram estimates are to be performed. Next, a pointwithin wedge region 620, for example, point 630, may be selected, and anestimate of the true (i.e., actual) scalogram value at point 630 may bedetermined based on scalogram values contained within vicinity region640. As shown in FIG. 6, vicinity region 640 may encompass both resolvedscalogram values (i.e., from resolved region 610) and previouslyestimated scalogram values (i.e., contained within wedge region 620),depending on the location of point 630 and the size (and shape, asdescribed below) of vicinity region 640. Vicinity region 640 may alsoinclude points for which no scalogram estimates have been taken. Suchpoints may be ignored, for example, set to the value zero or the value“undefined,” in computing an estimate of the scalogram value at point630.

Next, a new point in wedge region 620 may be selected, the vicinityregion correspondingly moved to match the location of the newly selectedpoint, and the estimation process described above may then be used toestimate the true value of a scalogram at the new point using thetechniques described above. This estimation process may repeat untilestimates of the true value of the scalogram have been estimated at asufficient number of points in wedge region 620. For example, theprocess may repeat until an estimate has been determined at each pointmarked with an ″ in wedge region 620. In an embodiment, multiple passesof the estimation technique described herein may be performed, and someor all of the points marked with an ″ in wedge region 620 may beestimated more than once, for example, during more than one pass. Thisapproach may be advantageous in exploiting scalogram estimates in alater pass than were not available in an earlier pass or for iterativelyrefining scalogram estimates. The number of passes performed may dependon computational resources available, the level of desired estimationaccuracy, and/or on the allowable time-delay in estimating scalogramvalues with wedge region 620. As shown in FIG. 6, not all points inwedge region 620 are directly estimated (e.g., in an embodiment, onlythose points marked with an ″ are estimated). Estimates of the truevalue of the scalogram for these points may be derived instead byinterpolating neighboring estimates (e.g., by interpolating estimates ofthe scalogram value taken at points marked with an ″ in scalogram 600).

In an embodiment, vicinity region 640 may be circular, as shown in FIG.6. However, the estimation scheme disclosed herein can be used with avicinity region of any suitable shape and/or size, including forexample, any polygonal shape, regular geometric shape, or an arbitraryshape. In an embodiment, the shape of vicinity region 640 may depend onthe location of the point to be estimated, for example, point 630,within the vicinity region and/or on the shape of the curved borderwhere the wedge region, for example, wedge region 620, meets theresolved region, for example, resolved region 610. For example, theshape of vicinity region 695 (FIG. 6B) is shaped to conform to the shapeof the curved border where wedge region 680, meets resolved region 697.

In an embodiment, the point at which the scalogram value is to beestimated, for example, point 630, may not be centered within thecorresponding vicinity region, but rather, may be located at any otherposition within, on the border of, or outside the corresponding vicinityregion. For example, scalogram 650 (FIG. 6B) illustrates an embodimentfor which the vicinity region, that is, vicinity region 670 (FIG. 6B),does not include the estimation point, that is, point 665 (FIG. 6B).Alternatively, scalogram 675 illustrates an embodiment for which thevicinity region, that is, vicinity region 695 (FIG. 6B), includes thepoint to be estimated, that is, point 690 (FIG. 6B), on the border ofthe vicinity region.

FIG. 7 depicts an illustrative process for estimating scalogram valuesin a wedge region, for example, wedge region 620 (FIG. 6B) in accordancewith an embodiment. Process 700 may start at step 705. At step 710, aportion of a suitable signal may be obtained, for example, using pulseoximetry system 10 (FIGS. 1 and 2) or system 400 (FIG. 4). The signalobtained at step 710 may be a PPG signal and/or any suitable biosignal.At step 720, a continuous wavelet transform of the signal obtained atstep 710 may be obtained. At step 730, the scalogram of the continuouswavelet transform may be generated or otherwise obtained. For example,the scalogram of the continuous wavelet transform may be generated orobtained using a processor such as processor 412 (FIG. 4) ormicroprocessor 48 (FIG. 2) and the computed scalogram may be displayedon a monitor such as monitor 26 (FIG. 1) or display 20 or 28 (both ofFIG. 1).

At step 740, an estimation scheme for estimating scalogram values in awedge region, such as wedge region 620 (FIG. 6A), may be determined. Forexample, various parameters of the estimation scheme may be determinedat step 740. The parameters of the estimation scheme may be set manuallyby an operator using user inputs 56 (FIG. 2), automatically by pulseoximetry monitor 14 (FIG. 1), or through a combination thereof. In anembodiment, parameters of the estimation scheme may depend on thebiological characteristics of patient 40 (FIG. 2). At step 750,scalogram values in the wedge region may be estimated. For example,scalogram values may be estimated using the estimation scheme determinedat step 740, and may be performed by pulse oximetry monitor 14 (FIG. 1)using processor 412 (FIG. 2) or microprocessor 48 (FIG. 2). Theestimated values of the scalogram may be displayed on a monitor ordisplay such as monitor 26 (FIG. 1) or display 20 or 28 (both of FIG.1). Step 750 may produce a “complete” scalogram, where the completescalogram is the scalogram obtained at step 730 with energy values inthe wedge region, for example, wedge region 620 (FIG. 6A), replaced bythe estimated scalogram values obtained at step 750.

At step 760, one or more signal parameters may be determined based onthe complete scalogram obtained at step 750. For example, signalparameters corresponding to the biological characteristics of patient 40(FIG. 2) may be determined, including oxygen saturation, respirationrate, and/or respiration effort. In an embodiment, noise parametersand/or noise characteristics of the signal obtained at step 710 may bedetermined at step 760. For example, noise parameters may be determinedby applying one or more filters or image processing algorithms to thecomplete scalogram, by using template matching, averaging, and/or anyother suitable technique. In an embodiment, noise may be removed fromthe complete scalogram or directly from the signal obtained at step 710,based on the determined noise parameters and/or noise characteristics.

At step 770, one or more confidence metrics may be determined, whereeach confidence metric corresponds to a measure of the accuracy and/orreliability of a parameter (or parameters) determined at step 760. Theone or more confidence metrics may be determined using, for example,using processor 412 (FIG. 4) or microprocessor 48 (FIG. 2). In anembodiment, each confidence metric may represent the statisticalprobability (or, for example, the empirically determined fraction oftime) that a parameter determined at step 760 is correct to within aspecified threshold. Alternatively, a confidence indicator may representa degree of confidence, measured on any suitable scale, that a parameterhas been correctly determined, and may be measured, for example, by amean square error criterion. A probability or confidence indicator maybe determined using, for example, Bayesian or Neyman-Pearson statisticaltechniques computed in processor 412 (FIG. 4), historical or trend datapreloaded or otherwise available in monitor 14 (FIG. 1), patientspecific medical information provided to monitor 14 (FIG. 1), userinputs 56 (FIG. 2), or any other suitable technique. At step 780, theone or more confidence metrics determined at step 780 may be comparedthresholds or any other suitable test, for example, including a binarytest. In an embodiment, the one or more confidence metrics may be testedto determine if they satisfy a constraint set. If the one or moreconfidence metrics are determined to be valid (for example, if the oneor more confidence metrics satisfy the constraint set), then process 700may proceed to step 790. If however, at least one of the tests carriedout at step 780 fails (for example, if a binary test fails), thenprocess 700 may return to step 740. At step 740, process 700 may resetparameters associated with the estimation scheme, for example, toimprove the performance of the estimation scheme. For example, process700 may increase the number of estimation points, increase thecomplexity (and therefore performance) of the estimation algorithm, orchange the size and/or shape of the vicinity region, as described above.

In process 700, steps 770 and 780 are optional, and if included, mayallow for iterative improvements in the quality of the one or moreparameters determined at step 760. If, however, steps 770 and 780 arenot included in an embodiment of process 700, then process 700 mayproceed to step 790 directly from step 760. In either case, at step 790,the one or more signal parameters determined at step 760 may be output.For example, the signal parameters may be output to a display such asmonitor 26 (FIG. 1) or display 20 or 28 (both of FIG. 1), through anaudible message provided through a speaker such as speaker 22 (FIG. 2),through a written printout, or through a combination of some of theseand other suitable techniques.

FIG. 8 depicts an illustrative process for determining a scalogram-basedestimation scheme in accordance with an embodiment. Process 800 may be afurther embodiment of step 740 of process 700 (both of FIG. 7). At step810, the number and location of estimation point within the wedgeregion, for example, wedge region 580 (FIG. 5), may be determined. Thenumber and location of estimation points may be based on specific systemand patient parameters and/or may depend on tunable parameters that canbe controlled by an operator, for example, using user inputs 56 (FIG. 2)to tune parameters viewable on a display such as monitor 26 (FIG. 1) ordisplay 20 or 28 (both of FIG. 1). If the number and location ofestimation points are chosen statistically, they may be chosen based ona density criterion, specified, for example, in terms of a number ofestimation points per scale and/or time. The desired density may betuned using user inputs 56 (FIG. 2). Alternatively or additionally, thenumber and location of estimation points may be determined based onfactors including the desired estimation quality, the computationresources available, and/or the maximum tolerable computational delay.The number and location of estimation points chosen at step 810 may bechosen as to provide estimates for the entire wedge region, for example,wedge region 580 (FIG. 5), or may be chosen relatively sparsely. In thelatter case, interpolative or other smoothing techniques may be used tocreate the completed scalogram based on the estimated scalogram values.

At step 820, an estimation technique, including related parameters, maybe determined. The estimation technique may be used to combine, weigh,interpolate, or otherwise parse data samples contained within thevicinity circle, for example, vicinity circle 640 (FIG. 6A), todetermine estimates of the true scalogram value at each point determinedat step 810. Any suitable estimation technique may be used. For example,two-dimensional surface interpolation may be used, or extrapolationtechniques from the full resolved region, for example, fully resolvedregion 610 (FIG. 6A) may be used. The vicinity circle, for example,vicinity circle 640 (FIG. 6A), may use sample points in both the fullyresolved region and the wedge region, for example, wedge region 620(FIG. 6A), to determine an estimate of the true value of the scalogramat a point, for example, point 630 (FIG. 6A). In an embodiment, anestimate at a point, for example, point 630 (FIG. 6A) may be made, atleast partially, by weighing data points within the vicinity circleaccording to degree to which each data point is resolved. For example,data points that are more fully resolved (i.e., located further to leftin a scalogram such as scalogram 550 (FIG. 5) may contribute more to afinal estimate of the scalogram value at the estimation point comparedto data points that are only partially resolved (i.e., located furtherto the right in a scalogram such as scalogram 550 (FIG. 5). Further, toestimate the value of the scalogram at a point such as point 630 (FIG.6A), a surface model may be built or referenced, and a two-dimensionalfunctional approximation to the surface model may be used, possibly inaddition to other techniques, to estimate the value of the scalogram atthe desired point.

At step 830, the size and shape of the vicinity region may bedetermined. For example, vicinity region 640 (FIG. 6A) may be used toestimate scalogram point 630 (FIG. 6A), vicinity region 670 (FIG. 6B)may be used to estimate scalogram point 665 (FIG. 6B), and vicinityregion 695 (FIG. 6B) may be used to estimate point 690 (FIG. 6B). Thesize and shape of the vicinity region may be set based on templatematching preexisting models of scalogram surfaces, on characteristics ofa biological parameter to be estimated, and/or on patientcharacteristics, in addition to any other suitable factor.

FIG. 9 depicts an illustrative process for estimating scalogram valuesin a wedge region, for example, wedge region 620 (FIG. 6A) using adetermined estimation scheme, for example, determined at step 740 ofprocess 700 (both of FIG. 7), in accordance with an embodiment. Process900 may correspond to a further embodiment of step 750 of process 700(both of FIG. 7). Process 900 may be used to iteratively estimatescalogram values in a structured grid pattern. For example, process 900may be used to estimate the scalogram value at each grid point markedwith an ″ in wedge region 620 of scalogram 600 (both of FIG. 6A). In anembodiment, process 900 may first estimate the value of the scalogram atpoint 645 (FIG. 6A), and then iteratively estimate scalogram values,proceeding from left to right within each row of wedge region 620 (FIG.6A).

At step 910, initial scale and time values may be set. In an embodiment,the initial scale and time values may be set to correspond to one of theestimation points determined at step 740 of process 700 (FIG. 7) or step810 of process 800 (FIG. 8). For example, an initial scale value may beset to the point s=s₀ and an initial time value may be set to a pointt=t₀, where s₀ and t₀ denote a starting point in a wedge region, forexample, point 645 in wedge region 620 (both of FIG. 6A).

At step 920, process 900 may estimate the true value of the scalogram atthe point selected at step 910. For example, if point 645 (FIG. 6A) isselected at step 910, then process 900 may estimate the true value ofthe scalogram at this point at step 920. Process 900 may use anysuitable technique to estimate the scalogram value at step 920,including any of the techniques described at step 820 of process 800(both of FIG. 8). At step 930, the current value of the time scale, t,may be compared to a maximum time value, t_(max). For example, as shownin FIG. 6A, time 642, that is, a time equal to t_(max), may representthe maximum (i.e., most recent) time scale value for which the scalogramis to be estimated. If the value of t is less than t_(max), then process900 may proceed to step 940. At step 940, the value of t may beincremented to the next value for which the scalogram is to beestimated. In an embodiment, the estimation points are placed in regularstructure (for example, as shown by the ″ marks in wedge region 620 ofFIG. 6A), and in this case, the value of t_(max) be incremented by aconstant value t_(step), where t_(step) is a positive number. If, atstep 930, the value of t equals the value of t_(max), then process 900may proceed to step 950. At step 950, the value of s may be incrementedto the next value for which the scalogram is to be estimated. Forexample, the value of s may first be compared to a maximum value,s_(max), shown in FIG. 6A as scale value 644. If the value of s is equalto the value of s_(max), then t=t_(max) and s=s_(max), indicating thatthe scalogram estimation procedure has completed estimating allscalogram points, determined, for example, at step 810 of process 800(both of FIG. 8). For example, in FIG. 6A, the estimation process mayhave enumerated all grid points with the last placed point being point641 (FIG. 6A). If at step 950, the value of t is determined to bet_(max), then process 900 may have finished estimated scalogram valuesalong a particular row of grid points that is not the last row. Forexample, process 900 may be at point 643 (FIG. 6A). In this case,process 900 may move to the first point on the next row, by setting t=t₀and by incrementing the value of s by s_(step). The value of t₀ maydepend on the current value of s, and may conform to the shape of thewedge region, for example, wedge region 620 (FIG. 6A).

The process described above is merely illustrative and variousalternations and changes could be made to the techniques describedabove. For example, grid points may be determined using a non-regularstructure. In this case, the iterative estimation scheme describedabove, and in particular steps 930, 940, 950, and 960 of process 900could be readily modified so that the values of t_(step) and s_(step)depend on the particular locations of grid points within a wedge region,for example, wedge region 620 (FIG. 6A). Similarly, the processdescribed above performs inner iterations across time, but could bereadily modified so that inner iterations are performed across scalevalues or any other suitable regular or irregular dimension.

FIG. 10 depicts an illustrative process for determining one or moresignal parameters and determining one or more confidence metrics inaccordance with an embodiment. Process 1000 may represent a furtherembodiment of steps 760 and 770 of process 700 (all of FIG. 7). At step1010, the energy values and energy structure in a scalogram pulse band,for example, pulse band 560 of scalogram 550 (both of FIG. 5) may becalculated. Energy values may be calculated by averaging the energydensities of a scalogram, such as scalogram 550 (FIG. 5), within a giventime-window or through any other suitable technique. For example, energymay be calculated by averaging the energy density only over those energyvalues below a certain percentile threshold in pulse band 560 (FIG. 5),or by averaging only the minimum or maximum values at each time instant.Alternatively, the energy structure in pulse band 560 (FIG. 5) may becalculated by recording the presence of features within a giventime-window such as the number of and frequency of repeated patterns,the presence of high energy regions followed by low energy regions,and/or any other suitable characteristics.

At step 1020, the energy values and energy structure in a noise band,for example, noise band 570 (FIG. 5) may be calculated. Energy valuesmay be calculated by averaging the energy densities of a scalogram, suchas scalogram 550 (FIG. 5), for example, within a given time-windowand/or through any other suitable scheme. For example, energy may becalculated by averaging the energy density only over energy values belowa certain percentile threshold in noise band 570 (FIG. 5), or byaveraging only the minimum or maximum values at each time instant.Alternatively, the energy structure in noise band 570 (FIG. 5), may becalculated by recording the presence of features within a giventime-window such as the number of and frequency of repeated patterns,the presence of high energy regions followed by low energy regions,and/or any other suitable characteristics.

At step 1030, one or more signal parameters may be determined from theenergy and structure results calculated at steps 1010 and 1020. Forexample, a respiration rate, oxygen saturation level, and/or respirationeffort level of a patient such as patient 40 (FIG. 2) may be determined.To determine the one or more signal parameters, curve fitting may beperformed on plots of energy values, energy structural characteristics,signal-to-noise levels, as well as on any other plots or other datatypes that may have been determined at step 1010 and 1020. The curvefitting may be done using linear least-squares fitting of data,higher-order interpolative techniques, or any other suitable technique.Parameterization and/or curve fitting can be performed, for example, byprocessor 412 (FIG. 4) or microprocessor 48 (FIG. 2), and mayadditionally depend on parameters entered by a user through user inputs56 (FIG. 2). At step 1030, the one or more signal parameters may bedetermined based on current data as well as from past data (e.g.,generated in previous iterations of process 1000). Such past data may bestored in, for example, ROM 52 (FIG. 2) and/or RAM 54 (FIG. 2).

At step 1040, one or more confidence metrics may be determinedcorresponding to the signal parameters determined at step 1030. Forexample, a confidence metric may be determined based on the energy andstructure results determined at step 1010 and/or 1020, and/or based oncurrent and/or past data from signal-to-noise level plots. Alternativelyor additionally, confidence metrics may be determined using tabulatedfigures or merit or through any other suitable scheme. Each confidencemetric may be represented by a number from 0 to 100, where a largernumber indicates a higher confidence level. Alternatively oradditionally, any suitable parsing, combining, or weighing strategy maybe used to combine the energy and/or structure results of steps 1010 and1020 to determine the one or more confidence metrics. For example,maximum-likelihood techniques may be used to combine data andNeyman-Pearson combining techniques may be used when the priorprobability of a signal quality decrease event is unknown. At step 1040,the one or more confidence metrics may be determined based on currentdata as well as from past data (e.g., generated in previous iterationsof process 1000). Such past data may be stored in, for example, ROM 52(FIG. 2) and/or RAM 54 (FIG. 2).

It will be understood that, while the above disclosure is made in thecontext of a medical signal processing application (i.e., based on oneor more PPG signals generated by a pulse oximetry system), the featuresof the present disclosure may be applied in the context of any signalprocessing application and may be applied to any suitable signal orsignals, such as, for example, biosignals (e.g., electrocardiogram,electroencephalogram, electrogastrogram, electromyogram, heart ratesignals, pathological sounds, ultrasound, or any other suitablebiosignal), dynamic signals, non-destructive testing signals, conditionmonitoring signals, fluid signals, geophysical signals, astronomicalsignals, electrical signals, financial signals including financialindices, sound and speech signals, chemical signals, meteorologicalsignals including climate signals, and/or any other suitable signal,and/or any combination thereof.

It will also be understood that the above method may be implementedusing any human-readable or machine-readable instructions on anysuitable system or apparatus, such as those described herein.

The foregoing is merely illustrative of the principles of thisdisclosure and various modifications can be made by those skilled in theart without departing from the scope and spirit of the disclosure. Thefollowing claims may also describe various aspects of this disclosure.

1. A method for processing a scalogram to estimate one or more energyvalues in a wedge region of the scalogram, the method comprising:receiving a signal; and using processing equipment for: transforming thesignal based at least in part on a continuous wavelet transform;generating the scalogram based at least in part on the transformedsignal; estimating the one or more energy values in the wedge region ofthe scalogram based at least in part on an estimation scheme;determining one or more signal parameters of the signal based at leastin part on the one or more estimated energy values; and outputting thedetermined one or more signal parameters to an output device.
 2. Themethod of claim 1, wherein estimating the one or more energy valuescomprises: determining a plurality of estimation points and a set oflocations corresponding to the plurality of estimation points in thewedge region of the scalogram; determining a set of estimationparameters corresponding to the estimation scheme; and determining asize and shape of a vicinity region.
 3. The method of claim 2, whereinthe determined size and shape of the vicinity region is based, at leastin part, on one or more characteristics of the one or more signalparameters.
 4. The method of claim 2, wherein the determined size andshape of the vicinity region is based, at least in part, on one or morecharacteristics of a patient.
 5. The method of claim 1, wherein thesignal comprises a photoplethysmograph (PPG) signal received from asensor.
 6. The method of claim 1, wherein the one or more signalparameters comprises a patient oxygen saturation level.
 7. The method ofclaim 1, wherein the signal parameter comprises a patient respirationrate.
 8. The method of claim 1, wherein the method further comprises:determining one or more confidence metrics based at least in part on theone or more estimated energy values; and determining if the one or moreconfidence metrics satisfy a constraint set.
 9. The method of claim 8,wherein determining the one or more confidence metrics comprises:determining energy values and energy structure in a pulse band of thescalogram; and determining energy values and energy structure in a noiseband of the scalogram.
 10. The method of claim 1, wherein the estimateof at least one energy value in the one or more estimated energy valuesis based, at least in part, on a set of resolved energy values in aresolved region of the scalogram and a set of estimated energy values inthe wedge region of the scalogram.
 11. A system for processing ascalogram to estimate one or more energy values in a wedge region of thescalogram, the system comprising: a sensor capable of generating asignal; and one or more processors coupled to the sensor, wherein theone or more processors are capable of: receiving the signal from thesensor; transforming the signal based at least in part on a continuouswavelet transform; generating the scalogram based at least in part onthe transformed signal; estimating the one or more energy values in thewedge region of the scalogram based at least in part on an estimationscheme; determining one or more signal parameters of the signal based atleast in part on the one or more estimated energy values; and outputtingthe determined one or more signal parameters to an output device. 12.The system of claim 11, wherein estimating the one or more energy valuescomprises: determining a plurality of estimation points and a set oflocations corresponding to the plurality of estimation points in thewedge region of the scalogram; determining a set of estimationparameters corresponding to the estimation scheme; and determining asize and shape of a vicinity region.
 13. The system of claim 12, whereinthe determined size and shape of the vicinity region is based, at leastin part, on one or more characteristics of the one or more signalparameters.
 14. The system of claim 12, wherein the determined size andshape of the vicinity region is based, at least in part, on one or morecharacteristics of a patient.
 15. The system of claim 11, wherein thesignal comprises a photoplethysmograph (PPG) signal received from asensor.
 16. The system of claim 11, wherein the one or more signalparameters comprises a patient oxygen saturation level.
 17. The systemof claim 11, wherein the one or more signal parameters comprises apatient respiration rate.
 18. The system of claim 11, wherein the one ormore processors are further capable of: determining one or moreconfidence metrics based at least in part on the one or more estimatedenergy values; and determining if the one or more confidence metricssatisfy a constraint set.
 19. The system of claim 18, whereindetermining the one or more confidence metrics comprises: determiningenergy values and energy structure in a pulse band of the scalogram; anddetermining energy values and energy structure in a noise band of thescalogram.
 20. The system of claim 11, wherein the estimate of at leastone energy value in the one or more estimated energy values is based, atleast in part, on a set of resolved energy values in a resolved regionof the scalogram and a set of estimated energy values in the wedgeregion of the scalogram.